Problem: Simplify the following expression: $z = \dfrac{n^2 - n - 12}{n - 4} $
Solution: First factor the polynomial in the numerator. $ n^2 - n - 12 = (n - 4)(n + 3) $ So we can rewrite the expression as: $z = \dfrac{(n - 4)(n + 3)}{n - 4} $ We can divide the numerator and denominator by $(n - 4)$ on condition that $n \neq 4$ Therefore $z = n + 3; n \neq 4$